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Two vertices of a triangle are (3,-2) an...

Two vertices of a triangle are (3,-2) and (-2,3) and its orthocentre is (-6,1) . Then the third vertex of this triangle can not lie on the line

A

6 x + y = 0

B

4x + y = 2

C

5x + y = 2

D

3x + y = 3

Text Solution

Verified by Experts

The correct Answer is:
C
Let A(h,k) be the third vertex of `Delta`ABC whose two vertices are B(3,-2) and C(-2,3) and orthocentre at P(-6,1) . Then AP is perpendicular to BC and BP is perpendicular to AC .
`therefore (k-1)/(h + 6) xx (3 +2 )/(-2 -3) = -1 ` and `(1 + 2)/(-6-3) xx (k-3)/(h + 2) = -1`
`implies h - k + 7 = 0` and `3h - k + 9 = 0`
`implies h = -1 , k = 6`
Clearly , these values of h and k do not satisfy 5x + y = 2 .
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